If the value of a $23,642 car decreases by 24% each year due to depreciation, how much will the car be worth after 14 years?

To calculate the value of the car after 14 years, given that its value decreases by 24% each year, we can use the formula for exponential depreciation:

\[
V = P \times (1 - r)^t
\]

where:
- $ V $ is the value of the car after $ t $ years,
- $ P $ is the initial value of the car (in this case, \$23,642),
- $ r $ is the depreciation rate (24% or 0.24),
- $ t $ is the number of years (14 years).

### Step-by-step Calculation:

\[
V = 23,642 \times (1 - 0.24)^{14}
\]

\[
V = 23,642 \times (0.76)^{14}
\]

Let's compute this value.

The value of the car after 14 years, given a 24% annual depreciation rate, will be approximately \$507.08.

Would you like more details on the calculation or any further explanation?

Here are 5 related questions for further exploration:
1. How would the car's value change if the depreciation rate was 20% instead of 24%?
2. What would the value be after 10 years instead of 14?
3. How can the formula be adjusted if the depreciation rate changes each year?
4. What would the car's value be after 5 years of depreciation at 24%?
5. How does exponential depreciation differ from linear depreciation?

**Tip:** Depreciation decreases faster at the start and slows over time because it's based on a percentage of the current value, not the original value.

Understand how to calculate the depreciation of a car using the exponential decay formula. This example problem explains how a $23,642 car depreciates by 24% annually and what its value will be after 14 years. Suitable for students in Grades 9-12.

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